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1. If the graph of y=x^3 + ax^2 + bx - 8 has a point of inflection at (2,0), what is the value of b?

2. Let f(x) be the function defined by f(x)= k + 12x + 3x^2 - 2x^3 where k is a constant.
a) On what interval is the function increasing? Justify your answer.
b) Find the interval where the function is concave up. Justify answer.

3. What are all values of x for which the graph of y=6x^2 + x/2 + 3 + 6/x is concave downward?

4. At what point on the curve x^3 - y^2 + x^2 =0 is the tangent line vertical?

5. A particle moves along the x-axis so that its position at any time t=0 is given by x(t)= t^3 + 22t + 3 - 6cos(π t). For what value of t is the velocity negative?
a. t=1/2
b. t=1
c. t=3/2
d. t=2
e. The velocity is never negative.

6. How many extrema (maxima and minima) does the function f(x) = (x+2)^3 • (x-5)^2 have on the open interval (-3,6)?

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